How to transform a strip in the vse in a non-uniform way?
Unfortunately there is no way to do this within the VSE.

The way you can deform an image (or video) is by tracking four points and making a plane track. Then in the compositor use the Plane Track Deform Node and add the image over your background.



Now step by step.


Open up the Movie Clip Editor either by changing one if the windows, or switching the layout to Motion Tracking.
After importing your background (I'll assume from now on that it is an image) set the start and end frame to 1. That will make it so that when you put out the trackers, it doesn't have to track anything.

CtrlLMB  to add the markers you will need four of them to make a plane track. (because we aren't really tracking it does not matter where they are.)

Select all the trackers with AA then go to the Solve tab and under the Plane Track heading press the Create Plane Track button. Then just drag the corners in to place.

With the plane track in place head over to the compositor, and set up your nodes like this.
Three important things to note: 


The Plane Track Deform Node, that is where all the data from the tracker gets in to the compositor. Make sure you fill out the Camera and  Plane Track fields, there should only be one of each, unless you made more then one plane track. 
The image to be overlayed through the plane track goes in the bottom socket of the Alpha Over node. 
You should not have a Render Layers node, if you do blender will try to render your 3D scene, and not just work with two images. 


Make sure your render resolution, over in the render tab of the properties window, matches the dimensions of your background image. Now just press render, or push F 12 you will get something like this.






I do know about the corner pin node, and what I described above is pretty much exactly what that node is used for. Except it is a pain to use, this method is much easier to position.